Given point (6,-10) how do you find the distance of the point from the origin, then find the measure of the angle in standard position whose terminal side contains the point?

1 Answer
Scott F.
Mar 26, 2017

See below

Explanation:

To find the distance to the origin you use the distance formula, #d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#.

Plugging in the coordinates of the given point and the origin, #d=sqrt((6-0)^2+("-"10-0)^2)=sqrt136=2sqrt34~~11.7#

To find the angle, get a reference angle using #tan^("-"1)(|y|/|x|)# and then analyze the point to find the correct quadrant.

#tan^("-"1)(10/6)~~1.03# and since the point lies on the line below, it is in Quadrant #"IV"#. The value of an angle in Quadrant #"IV"# is #2pi-alpha# where #alpha# is the reference angle, so the angle for this point is #5.25#.

graph{-5x/3 [-1, 23, -11, 1]}

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